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Question

A lift is tied with thick iron wire and its mass is $$1000 kg$$. If the maximum acceleration of the lift is $$1.2 ms$$$$^{-2}$$ and the maximum stress of the wire is $$1.4$$ x $$10$$$$^{8}$$ Nm$$^{-2}$$, what should be the minimum diameter of the wire ?


A
102 m
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B
104 m
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C
106 m
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D
0.5 x 102 m
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Solution

The correct option is A 10$$^{-2}$$ m
$$ Stress \times area = M (g + 1.2)$$
$$1.4 \times 10^{8} \times \dfrac{\pi}{4}d^2 = 1000(11)$$
$$ {d^{2}} = \dfrac{1000  (11)\times 4}{\pi \times 1.4 \times 10^{8}}$$
$$d = \sqrt{\dfrac{4 \times 1000 (11)}{\pi \times 1.4 \times 10^{8}}}$$
$$d=\sqrt{\dfrac{10^4}{10^8}}$$
$$ = 10^{-2}m $$

Physics

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